Fraction to Decimal Calculator
Write a fraction or mixed number as an exact decimal, with the repeating digits marked, and rounded to the number of places you choose.
Result
Decimal, repeating block in brackets: 0.(142857)
A repeat that would run past 100 decimal places is not bracketed: the first 100 places are shown, ending in …, and the block’s length is given below.The bracketed decimal is exact. Only the rounded line is rounded, half away from zero.
- With a bar over the repeating digits
- 0.1̅4̅2̅8̅5̅7̅
- Rounded
- 0.1428571429
- Digits that repeat
- 6
- 0 means the decimal ends.
- Digits before the repeat starts
- 0
- Fraction in lowest terms
- 1/7
- As a percentage
- 14.2857%
https://calcgallery.com/notation-conversions/fraction-to-decimal-calculator/
Unit conversions follow from exact definitions and published notation rules. Sizes follow published standards and are approximate: makers grade their own, so check their chart. Figures are rounded only for display. Read the full disclaimer
How to use the Fraction to Decimal Calculator
- Enter the numerator and the denominator. For a mixed number such as 2 3/8, put the 2 in the whole number box.
- Choose how many decimal places to round to, for the line you would copy into a spreadsheet or onto a form.
- Read the exact decimal with its repeating digits marked, how many digits repeat, and the rounded value.
Long division, with a memory
Dividing by hand, each step brings down a zero and leaves a remainder smaller than the denominator. There are only so many possible remainders, so sooner or later one comes round again, and from that point the digits repeat exactly as before. The page does the same division with whole numbers, so no digit is lost to rounding, and marks where the repetition starts.
first = reduce the fraction to lowest termsdecimal digits = long division of numerator ÷ denominatorrepeat starts = after as many digits as the larger power of 2 or 5 in the reduced denominatorrepeat length = smallest k with 10^k − 1 divisible by the rest of the reduced denominatorThe fraction must be reduced first. 3/6 has a 3 in its denominator, which would predict a repeat, but it is 1/2, and 1/2 is 0.5 exactly.
For 5/12 the denominator is 2² × 3, so two digits come before the repeat and the 3 gives a block of length one: 0.41(6).
Rounding is a separate step
The bracketed decimal is exact. The rounded line cuts it to the number of places you choose and rounds half away from zero, so 1/8 to two places is 0.13 rather than 0.12. Rounding a repeating decimal always leaves a small error; to see how big, turn the rounded value back into a fraction with the decimal to fraction calculator, which also does the reverse of this page when the repeating digits are known.
With your numbers
- In lowest terms: 1/7
- Long division repeats a remainder after 0 + 6 digits
- Decimal = 0.(142857)
Quick reference
The bracketed decimal is exact. Only the rounded line is rounded, half away from zero.
| Example | Decimal, repeating block in brackets |
|---|---|
| 1/7 | 0.(142857) |
| 1/3 | 0.(3) |
| 5/12 | 0.41(6) |
| 3/8 | 0.375 |
| 22/7 | 3.(142857) |
| 2 3/8, a mixed number | 2.375 |
| 1/8 to 2 places | 0.125 |
| 1/97 | 0.(010309278350515463917525773195876288659793814432989690721649484536082474226804123711340206185567) |
Common questions about the Fraction to Decimal Calculator
- How do I turn a fraction into a decimal?
- Divide the numerator by the denominator. 3/8 is 3 ÷ 8 = 0.375. When the division never comes out even, the digits settle into a block that repeats forever: 1/7 is 0.142857142857…, written 0.(142857).
- Which fractions give repeating decimals?
- Reduce the fraction first. If the denominator then has no prime factors other than 2 and 5, the decimal ends; otherwise it repeats. 3/8 ends because 8 is 2 × 2 × 2. 5/12 repeats because 12 is 2 × 2 × 3, and the 3 can never be divided out by a power of ten.
- How long can the repeating part be?
- At most one less than the denominator. 1/7 repeats every 6 digits and 1/97 every 96. The page counts the block even when it is far too long to print, and writes out the first 100 decimal places.
- What do the brackets and the bar mean?
- Both mark the digits that repeat. 0.41(6) and 0.416 with a bar over the 6 both mean 0.41666… for ever. The brackets are easier to type; the bar, called a vinculum, is the other usual way to write it.
- How is a negative mixed number read?
- As a single negative number: −2 3/8 is −(2 + 3/8), which is −2.375. Put the minus sign on the whole number and leave the fraction unsigned.